Physical Chem Topic 2

Properties of Gases

• Understanding gas properties helps in the study of chemical reactions.

• Gases are simple systems; insights gained from them can help model more complex systems.

• Key questions include:

  • How do the number of gas molecules relate to the volume at a certain pressure and temperature?

  • How does pressure change with varying volume or temperature?

Ideal Gases

1. Pressure

• Definition: Pressure is the force per unit area from molecules colliding with container walls.

  • Depends on:

    • Molecular velocity: Faster molecules increase pressure through more frequent collisions.

    • Container size: Smaller volumes lead to more frequent wall collisions.

2. Pressure Units

• Consistency is crucial in calculations:

  • 1 atmosphere = 101325 Pascal (N m\u207B²) = 1.01325 bar = 760 Torr (or mm Hg)

3. States of Matter

• Solid:

  • Particles tightly packed, ordered, with strong attractions.

  • Fixed volume; diffusion is nearly impossible.

• Liquid:

  • Particles close but unordered; moderate attractions.

  • Fixed volume, able to diffuse.

• Gas:

  • Particles spaced widely, free to move about; weak attractions.

  • No fixed shape or surface; readily compressed and expands on heating.

4. Gas Laws

4.1 Boyle's Law

• Equation:

  • PV = constant

  • P1V1 = P2V2 (Pressure inversely proportional to volume at constant temperature)

• Practice:

  • Graph of P vs. 1/V to test Boyle's Law.

4.2 Charles' Law

• Equation:

  • V/T = constant (Temperature must be in Kelvin)

  • V1/T1 = V2/T2

• At constant volume, increasing temperature raises pressure due to more energetic collisions.

4.3 Avogadro's Principle

• Equation:

  • V/n = constant (Volume per mole of gas at fixed temperature and pressure is the same for all gases)

  • V1/n1 = V2/n2

• Molar volume at STP is approximately 22.4 dm³ per mole.

5. Ideal Gas Equation

• Equation:

  • PV = nRT

  • Where R = 8.314 J K\u207B¹ mol\u207B−1

• All units must be consistent; use SI units for coefficients.

6. Combined Gas Law

• Equation:

  • P1V1/T1 = P2V2/T2

• This relates the variables for a fixed mass of gas transitioning between different states.

7. Real Gases

• Real gases show deviations from ideal behavior under certain conditions (high pressure, low volume).

Van der Waals Equation

1.1 Volume Correction

• Real volume (Vreal) accounts for the space occupied by gas molecules:

  • Vreal = Videal + nb (where n is the number of moles)

1.2 Pressure Correction

• Real pressure accounts for intermolecular attractions:

  • Preal = Pideal - a(n/V)²

1.3 Constants

• Constants 'a' and 'b' in the Van der Waals equation differ for each gas and indicate real behavior deviations.

P-V Isotherms

• The graph of pressure versus volume at different temperatures shows real gas behavior.

  • Low temp = potential changes into liquid due to attractive forces.

Dalton's Law of Partial Pressures

• Equation:

  • P = PA + PB + PC (total pressure equals the sum of the partial pressures)

• In a mixture, partial pressure relates directly to the amount of gas present.

  • Mole fraction is calculated:

    • xA = nA/(nA + nB + nC)

Intermolecular Forces

• Interactions between molecules affect gas properties.

Types of Intermolecular Forces

• Dipole Moment: Occurs in polar molecules, dependent on electronegativity differences.

• Induction Forces: Temporary dipoles arise due to proximity of polar molecules to non-polar molecules.

• London Forces: Present in all molecules, increases with the size of the molecule.

Unique Properties of Water

• Strong hydrogen bonds lead to high boiling point and unusual expansion upon freezing.

Kinetic-Molecular Theory of Gases

• Relates gas behavior to molecule properties (velocity, kinetic energy, collision frequency).

Key Equations

• Velocity:

  • Mode: v* = √(2RT/M)

  • Mean: v̅ = √(8RT/πM)

  • Root Mean Square: vrms = √(3RT/M)

Kinetic Energy

• KE = 1/2 mv²; for gases, KE simplifies to KE = 3/2 kT.

Tutorial Questions

• Various practical applications and calculations related to gas laws and properties.